• Title/Summary/Keyword: circle foliation

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MINIMAL AND CONSTANT MEAN CURVATURE SURFACES IN 𝕊3 FOLIATED BY CIRCLES

  • Park, Sung-Ho
    • Bulletin of the Korean Mathematical Society
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    • v.56 no.6
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    • pp.1539-1550
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    • 2019
  • We classify minimal surfaces in ${\mathbb{S}}^3$ which are foliated by circles and ruled constant mean curvature (cmc) surfaces in ${\mathbb{S}}^3$. First we show that minimal surfaces in ${\mathbb{S}}^3$ which are foliated by circles are either ruled (that is, foliated by geodesics) or rotationally symmetric (that is, invariant under an isometric ${\mathbb{S}}^1$-action which fixes a geodesic). Secondly, we show that, locally, there is only one ruled cmc surface in ${\mathbb{S}}^3$ up to isometry for each nonnegative mean curvature. We give a parametrization of the ruled cmc surface in ${\mathbb{S}}^3$(cf. Theorem 3).